'Physics' of Baseball 4: Stealing Directions, Not Signs

Welcome to "’Physics’ of Baseball 4: Stealing Directions, Not Signs," another co-authored work by Realmenwearpurple of Purple Row and Keithsmoustache of Amazin’ Ave. In previous installments of this continuing series, we have investigated ways to use the gravitational field of players and fans to a team’s advantage. Gravity and other physics of the ballplayer/Earth system have several other effects upon the game, most notably with the stolen base. Join after the jump to see how stealing can really weigh on a player.

When running between bases player will have a velocity vector pointing in the direction they are traveling, with a magnitude of whatever their speed may be.  For now, we will just assume the base runner to be Bengie Molina, making the magnitude of the vector to be on the "glacial" order of magnitude, leading to the name: Vglacier. We will also assume the location to be Dodger Stadium in LA. The direction depends upon which bases the said "runner" (quite the misnomer in the case of Molina) is attempting to travel between.  Due to the orientation of MLB fields, the direction from first to second will always be some combination of north, east, or west. Many people believe this is because ballparks are planned so the sun will never be in a hitter's eyes during a day game, however, this study will introduce other likely factors. If we assume the direction from first to second is north (as is the case at 14 of the 30 MLB stadiums, including Citi field) the velocity vector of the "runner" is now Vglacier *north unit vector. When this vector is written in the non-inertial topocentric inertial frame and includes effects from the rotation of the Earth, the absolute velocity will have the following components:

Vabsolute=Ω(Earth Radius +altitude)in the east direction and Vglacier in the north direction.

Following a mess of math that no one wants to see and I really don't want to type here, this results in an absolute acceleration with components in the west and upward directions. This result means the normal force acting upon the player is significantly reduced! Bengie Molina reduces the total normal force acting to keep him from plummeting to Hell/the center of the Earth (he is already in LA, afterall) by running north between the bases. Notice if the signs were switched, that is if the player were running south, the normal force would actually be greater.  The normal force will be called "gravity" from now on because it counteracts the actual gravitational force.  Also, we see that running east or west does not affect this force at all, only running north or south. This means a player running north will be "lighter" than the same player running south. Easiest weight loss program ever. Someone needs to tell Pablo Sandoval.

Each stadium in MLB was analyzed to determine field orientation. These are, in the format (direction from first to second, second to third), (E-N), (N,W), (NE,NW), and (NW,SW).  Using the SB totals for each of the 30 MLB teams for the 2007-2010 seasons (large enough sample size to shut up critics of our scientific method and to cancel out all the unpredictable gravitational forces we discussed in Physics of Baseball 2), an average number of SB per team was found for each orientation. Figure 1 is very telling, showing that it is indeed much more difficult to steal bases for teams whose home ballparks include a south-component to the direction between commonly steal-able bases (from first to second or second to third), with only 302.5 SB per team on average.  This number skyrockets to 325.25 stolen bases per team for those who play their home games in a ballpark where stealing bases ALWAYS involves a north component, assisting base-stealers on every attempt.

Figure 1. 4-year Average Total SB by Stadium Orientation

While these results are shocking, and may lead prolific base-stealers to reconsider stealing bases (especially third) in ball parks in Colorado, Arizona, San Diego, Toronto, Philadelphia, and Cleveland, they would be wise to reconsider abandoning their life of (base path) crime. There is a second factor which will affect the potential of being caught in the act, something Tiger Woods wishes he knew about last Thanksgiving.

Since travel in a northwards direction yields decreased "gravity," and south leads to increased "gravity," we can see there are some distinct differences in gravitational effects on the runner given stadium orientation.  In the E-N system, stealing second is considered neutral because east-west motion does not influence the force of "gravity."  However stealing third leads to lower g-force on the runner due to the northwards motion.  On the other hand, the N-W configuration means the runner will be decreasing in force of "gravity" when taking second base, but will have no added effects when taking third.  The NE-NW system has a partial northern component when stealing either base, but since the direction isn't directly north, only a fraction of the total "gravity" penalty is achieved when stealing either base.  Finally the NW-SW system is beneficial to stealing third base due to the partially south-oriented vector.  However the NW direction of first base from there means "gravity" is increased.

Figure 2. 4 year average caught stealing data for each of the 4 orientations.

The average number of times caught stealing per year averaged over 4 years, as seen in Fig. 2, is greatest when the runner is running north from first to second base.  The second worst caught stealing rate occurs when the runner runs north from second base to third.  Parks in which all base stealing is done in a northeast or northwest direction have a lower base stealing penalty due to only partially north trajectory, while parks where third base is stolen in a southwestern direction and second base is only partially north-oriented has the lowest stolen base penalty due to the "gravity" bonus of running south.  This establishes that increased "gravity" force has a paradoxically beneficial effect on caught stealing rates for a team.

Now that we have established that the equivalent "gravitational force" on the player is greatest when traveling in a southward direction, we next investigated the effect of this gravitational force on caught stealing rates.  Upon initial observation, the caught stealing rate actually appears to be helped by an increasing "gravitational force" on the baserunner.  Under the rules of classical physics, this seems to be counterintuitive, as increased "gravitational force" means greater energy is required to run between bases.  As such we are required to utilize a non-classical physics model to explain these opposing results. 

To this end we look to relativistic time dilation, specifically gravitational time dilation.

                  Figure 3. The most important Albert in baseball history

Gravitational time dilation is a principle of relativistic physics in which differences in gravitational fields lead to differences in the observed rate of time passage.  Due to the principle of equivalence, an accelerated reference frame (in this case the runner as his normal gravitational force increases) can be considered the same as a gravitational field, and can be treated as a source of gravitational time dilation.  Under gravitational time dilation, time will move more rapidly inside the accelerated reference frame compared to the outside observer.  As such the baserunner moving south will essentially see himself moving at normal speed and everything outside himself in slow motion, while the outside observer (pitcher or catcher) sees themselves as moving at normal speed, but the baserunner as moving very fast.  Conversely movement in a direction which decreases the g-force on the baserunner (North) would have the opposite effect.

This means that time dilation gives a twofold advantage to the runner assuming he is moving in a direction which enhances the g-force on the runner.  First since the outside world is in slow motion compared to the reference frame of the runner, the pitcher moves very slowly, leading to a better read on his delivery, and a better jump on the subsequent stolen base attempt.  Furthermore, the runner would be moving at a greater velocity outside of the time dilation field than he seems to be in the time dilation field, since he covers the same distance in less time outside of the field than he does inside of it.  This leads to an increase in runner velocity from the perspective of the pitcher or catcher, giving him a quicker base to base transit.  On the other hand, if the runner is heading north, time will be passing more slowly for the runner compared to the pitcher/catcher, thereby making it more difficult to get a good read on the pitcher, and lengthening the transit time between bases.

Some exceptions obviously exist with such complex physical phenomena occuring.  A few teams seem to fall outside of the expected trend in this regard.  The Pirates for example are ~20% below average in caught stealing for their directional demographic.  It is pretty obvious why the Pirates have a clear advantage in not getting caught stealing.  By their very nature pirates are thieves, adept at claiming treasure for their own.  With centuries of thieving knowledge passed down from the likes of Blackbeard, pirates are naturals at swiping bases.

 Figure 4. Tim Redding knows how to steal a base...and your heart

Another team which clearly falls outside of the expected trend is the Tigers.  Again the Tigers have a much lower than expected rate of caught stealing given their stadium orientation.  Given their location in Detroit, I would imagine the players are simply attempting to escape the city, one base at a time.  It's amazing what a little added motivation can do.

The A's have a lower than expected caught stealing rate as well.  The name may suggest this is due to their outstanding athletic ability.  In actuality, the A's have the youngest roster on baseball (28.3 years old on average).  This suggests the A's have discovered the fountain of youth.  By making all of their players exceptionally young, they are physically more capable of overcoming the gravitational limitations of their stadium than any other team.  Given the tendency of people to avoid Oakland at all costs, it is unsurprising that outsiders have not yet discovered the secret of this city.

The Rockies are caught stealing more than any team in the NW/SW bracket.  Despite having the best gravitational advantage, the incessant dancing of Dinger is too distracting to allow the runners the concentration required to steal a base.  Many stolen base attempts by the Rockies are actually just players running towards Dinger in the stands in a burst of homicidal rage over his maddening antics.  This leads to an inordinate amount of outs on the basepaths.

Finally the Mets have an above average caught stealing rate for their stadium orientation.  It is surprising the Mets would be so bad at stealing bases, given how they've been excellent at robbing fans of their dignity, money, and hope for years now.  The most likely reason the Mets are caught so often is because they're never actually intended to steal.  With a runner on first, the Mets players know they have guaranteed an out, as Jerry will bring in Gary Matthews Jr Alex Cora to bunt.  Therefore the only way to prevent Jerry from wasting an out is to get to second before he can call for the bunt.  This causes the Mets to run wild on the basepaths, increasing both stolen bases and caught stealing stats.

Join us again soon for "Physics" of Baseball 5.